Submarine hovering system



April 27, 1965 H. c. SCHINK SUBMARINE HOVERING SYSTEM 3 Sheets-Sheet 2Filed May 3, 1961 DIFFERENTIATOR F|G.2A.

ERROR COMP UTOR l I l DIFFERENTIATOR INVENTOR HOWARD CHABFYKLES SCH l NK )2, MWMLL HIS ATTORNEYS April 27, 1965 H. c. SCHINK SUBMARINE HOVERINGSYSTEM Filed May 3, 1961 3 Sheets-Sheet 3 .l|||ll|.||| Illlllllll i1lllllll llllllllllllllll COMPOSITE SIGNAL GENERATOR i i I .i OUTIPUTTRANSLATOR I32 L- -'T ADl DER INVENTOR HOWARD CHARLES SCH l N K H [SATTORN EYS United States Patent This invention relates to a submarinehovering system and, more particularly, to a system that automaticallypositions a submarine accurately at a predetermined depth. I

A submarine is oftentimes required to assume a given depth in the oceanwhich theoretically requires a condition of neutral buoyancy. For anumber of reasons, including the temperature gradient of the water, thesalinity of the water, underwater currents, and the like, it isimpossible to maintain a true condition of neutral buoyancy. Therefore,the state of neutral buoyancy is approached by alternately flooding andexhausting water tanks in the boat.

During flooding and pumping operations, the boat momentarily achieves astate of neutral buoyancy, and then, depending on whether it isreceiving or exhausting water, becomes either heavier or lighter thanthe volume of water it displaces. When the submarine takes on sufiicientwater so that its density exceeds that of the volume of water itdisplaces, the boat sinks. Due to increasing water pressure as it sinks,the submarines hull contracts, thereby further increasing its densityand downward velocity. The converse is true when the boat becomespositively buoyant; i.e., its upward velocity increases as the depthdecreases.

Prior systems employed to position submarines at pre:

determined depths have generally taken into account one or more factorsthat include the Water pressure at the level actually assumed by theboat, the water pressure at the desired depth, and the rate of change indepth of the submarine. These factors were then combined in variousfashions to provide a single or a number of control signals to changethe buoyancy of the submarine. However, none of the prior art systemshas been successful in varying the buoyancy of a submarine to positionit rapidly and accurately at a desired depth without substantialundesirable hunting.

In the present invention an error signal, indicative of the differencebetween a depth actually assumed by a submarine and a desired depth, andits first and second time derivatives are combined after being suitablyweighted in accordance with the magnitude of the error signal to resultin the production of a single control signal that is used to repositionthe submarine. In this fashion, a given difference between a depthassumed and a depth desired results in a more than proportionatelylarger control sig nal than that produced by a smaller difference, andthe depth correction of the submarine is made much more rapid as theerror increases. This ensures that large errors are rapidly reduced,thereby increasing the effectiveness of the automatic control system.

Although the invention has been described generally above, a betterunderstanding-of it may be obtained by consulting the following detaileddescription of an exemplary embodiment thereof, when taken inconjunction with the appended drawings in which:

FIGURE 1 is a block diagram of an exemplary control system embodying theprinciples of the present invention for use in submarines; and

FIGURES 2A and 2B are detailed diagrams of selected ones of the blocksof FIGURE 1.

Referring to FIGURE 1, an exemplary automatic control system for thehovering of a submarine at a predetermined depth within the sea isshown. A signal indicative of the actual pressure exerted by the seawater at the depth actually assumed by the submarine is applied via aninput line 11 to an error computer 12. A signal indicative of thepressure exerted by the sea water at the depth at which it is desired toposition the submarine is applied to the error computer via an inputline 13. The error computer generates an output signal equal to thedifference between the two applied signals, i.e., the output signal isrepresentative of the ditference between the actual and ordered depthsof the submarine, hereinafter referred to as the depth error.

The output signal from the error computer 12 is applied to adifierentiator 14, to an instrumentation block 15, and to a gain deviceIt: located within a composite signal generator 17. Within theditferentiator 14-, the error signal is differentiated with respect totime to produce what may be termed a velocity signal. That is, when theordered pressure signal applied on line 13 to the error computer 12remains constant, the output signal from the difierentiator 14 is equalto the vertical velocity of the submarine, i.e., the rate of change inthe submarines depth. When the ordered pressure signal is changing,however, to call for a changing depth, such as a constantly increasingdepth, for example, the signal from the dififerentiator 14 is notindicative of the rate of change in the depth of the submarine. Thus,while the output signal from the difierentiator 14 is herein termed avelocity signal, the true nature of the signal should be kept in mind atall times, and it should be remembered that the signal represents therate of change, with respect to time, of the output signal from theerror computer 12.

The output signal from the differentiator 14 is applied to theinstrumentation block 15, to a difierentiator 18, and to one input of anadder 19. Within the ditferentiator 18, the output signal from thedifferentiator 14 is differentiated with respect to time to produce asignal equal to the second derivative of the depth error signal from theerror computer 12. This second derivative signal may be termed anacceleration signal; however, like the velocity signal, the accelerationsignal only represents the vertical acceleration of the submarine if theordered pressure signal applied to the error computer remains constant.

The output signal from the difierentiator 18 is applied to theinstrumentation block 15 and to the adder 19. The instrumentation block,which has applied thereto the depth error, velocity, and accelerationsignals, comprises any number of test instruments located at a centrallocation or at varied locations within the submarine to facilitatemonitoring the signals from the error computer and the dififerentiators.

Within the adder 119 the signals from the differentiators 14 and 18 aresummed together to produce a single output signal which is applied toone input of an adder 20 located within the composite signal generator17. Applied to the other input of the adder 20 is the output signal fromthe gain device 16. This latter signal is equal to the signal from theerror computer 12 modified in magnitude in accordance with the magnitudeof the error signal itself. This modification is such as to increaseproportionally the magnitude of the error signal by a larger amount whenthe error signal is large than when the error signal is small.

The output signal from the adder 20, i.e., the output signal from thecomposite signal generator 17, thus is equal to the sum of the velocity,acceleration, and the modified error signals. This output signal may beexpressed by the following equation:

dE d E where C is the output signal from the composite signal arenas?portionality factor determined by the magnitude of the depth errorsignal itself, 1 is time, and d is the differential operator.

The output signal from the composite signal generator takes allpertinent factors properly into consideration. By adding to the velocityand acceleration signals a modified depth error signal, a greatercorrection is provided when a greater depth error obtains. Furthermore,rapid changes in the depth error signal are reflected in the velocityand acceleration components of the composite signal, and thus changes inthe depth of the submarine are more quickly instituted when warranted byrapidly changing conditions.

The output signal from the composite signal generator 17 is applied toan output translator 2 1 which serves to transform the signal into asignal of any desired parameter. Thus, for example, if the signal fromthe composite signal generator is pneumatic or hydraulic, the outputtranslator 21 translates such a signal into an electrical signal if sodesired. Output signal translation is optional, however, and the controlsystem may deal entirely with signals of a single parameter.

The signal from the output translator 21 is applied to a servomechanism22 which in turn controls a pumping mechanism 23. The pumping mechanismpumps sea water both away from and into a hovering tan 22.4 used tocontrol the buoyancy of the submarine. Thus, for

example, when the depth error is positive, i.e., when the,

submarine is at a greater depth than that which is ordered, sea water ispumped out of the hovering tank into the sea in order to lighten thesubmarine. On the other hand, when the depth error is negative, i.e.,when the submarine is at a depth less than that ordered, sea water ispumped by the pumping mechanism into the hovering tank to add weight tothe submarine.

Turning now to FIGURES 2A and 23, a detailed d scription of exemplaryapparatus incorporated in selected ones of the blocks of FIGURE 1 willbe given. This apparatus is suitable for an automatic control system ina submarine, and, as shown, basically comprises a pneumatic system.

Error computer In FIGURE 2A, sea water obtained from an input port onthe side of a submarine (not shown), or a pneumatic pressurecorresponding to the pressure exerted by the sea water at the depthactually assumed by the submarine, is applied on an input line 25 to theerror computer 12. Within the computer the input line 25' is applied toone input 26 of a gage 27 and to one input 28 of a sensing bellows 29.

Pneumatic pressure from a source of reference pressure (not shown) isapplied on an input line 30 to the error computer 12. Within thecomputer, the pressure is adjusted by a pressure adjusting valve 31 toprovide an output pressure which is indicative of the depth at which itis desired to position the submarine. This output pressure is applied toan input 32 of the gage 27 and to an input 33 of the sensing bellows 29.

In the gage 27, the relative positions of two pointers 34 and 35 areindicative of the difierence between the depth at which it is desired toposition the submarine and the actual depth assumed by the submarine.For example, as shown in the figure, the pointer 34 is higher than thepointer 35, and thus the submarine is at a greater depth than that atwhich it is to be positioned. On the other hand, if the pointer 35 ishigher on the gage than the pointer 34, the submarine is above the depthat which it is to be positioned. In this fashion, the gage gives avisual indication of the depth error, and the gage may be located at anyconvenient point in the submarine for a quick visual inspection.

Within the sensing bellows 29 of the error computer 12, the twopneumatic pressures applied to the inputs 28 and 33 operate against eachother through two belows sections 36 and 37. A red 33 that couplestogether he two sections thus is forced either to the right in thefigure or to the left depending upon which of the pressures in the inputlines 23 and 33 is increasing relative to the other. For example,movement of the arm to the left indicates that the pressure applied tothe input 28 is increasing relative to the pressure applied to the input33. If the magnitude of the pressure applied to the input 28 is greaterthan the magnitude of the pressure applied to the input 33 at this time,this would indicate that the submarine is at a depth greater than thatordered and that the depth error is increasing.

The right and left movement of the rod 33 is translated by linkages 39,4t) and 41 into a pivotal movement of a nozzle regulating vane 42 abouta pivot point One end of the vane is positioned above a nozzle :4 thatexhausts air supplied thereto from a source of reference air pressure(not shown) that is supplied upon an input line 45 to the error computer12. The air pressure from the input line is first applied to a filter 46from which it passes to the nozzle 44 through a restriction 27 in nozzletube 48. The air pressure from the filter ie is also applied to an input49 of a booster section 59.

The booster section 50 consists of three bellows sections 51, 52, and53. The lower bellows section 51 is itself formed from two separatesections: an outer section 51' and an inner section 51". The outerbellows section 51 is coupled to an input line 54 that is connected tothe nozzle tube 48 just above the restriction 47. The middle bellowssection 52 and the upper bellows section 53 are both controlled by airpressure supplied thereto by a pressure line 55 that is coupled to anoutput line 56 of the booster section.

A connecting member 57 joins the middle and lower bellows sections 52and 51, and within the connecting member 57 a passage 53 permits a flowof air therethrough to the inner bellows section 51 that is dischargedthrough a discharge port 59. A valve member 60 is situated below thepassage '58, and regulates the flow of air therethrough as well as theflow of air from the line 49 through a passage 61. A base platform 62 iscoupled to the upper bellows section 53 and serves as a rest upon whichthe pivot 43 is positioned.

The operation of the error computer is as follows. Assume that thesubmarine is at a greater depth than that which is ordered and that theactual depth is increasing. In this instance, the rod 38 within thesensing bellows 29 moves to the left as shown by the arrow, and themovements of the linkages 39, 40, and 41, and the nozzle regulating vane42 are as shown by their associated arrows. The movement of the end ofthe nozzle regulating vane thus is toward the nozzle 44. This restrictsthe flow of air from the nozzle, thereby increasing the air pressuretherein.

The increased air pressure within the nozzle 44 is communicated to thelower, outer bellows section 51' through the line 54, and the section 51along with the connecting member 57 are moved downward. As theconnecting member is moved downward, it contacts the valve 60 pushingthe valve downward. This action closes off the passage 58 within theconnecting member andopens up the passage 6-1 to allow the flow ofadditional air to the chamber surrounding the lower bellows section 51and to the chamber between the bellows sections 52 and 53 through lines56 and 55. Since bellows sections 5-1 and 52 are substantially equal indiameter, the degree of opening of the passage 61 is not influenced bythis pressure change. The increase in pressure, however, causes theupper section 53 to be urged upward. The support plat- .form 62 isaccordingly raised upward, moving the end of the regulating vane 42 awayfrom the nozzle 44, thereby decreasing the pressure in the nozzle. Thisreduces the downward movement of the bellows section 51 and reduces theflow of air through the passage 61 to the output line 56.

Feb-- the use of feed back, the rapid and large change is tapered offsomewhat so that a balance condition is achieved, and

the output pressure from the booster section, i.e., the

depth error signal, is made to be exactlythat as called for by theparticular depth error. In this respect it should be noted that theoutput pressure varies about some fixed pressure that corresponds tozero depth error.

Difierentiator 14 The pneumatic depth error signal, after first passingthrough a filter 63 and an adjustable pulsation dampener 64, is appliedvia an output line 65 to the differeutiator 14, to the instrumentationblock 15, and to the composite signal generator 17. (See FIGURE 28.)Within the differentiator 14, the depth error signal is applied directlyto a bellows 66 and indirectly to a bellows 67 after first passingthrough a pressure dampening device 68. Because of the action Glf thepressure dampening device, for a changing depth error signal thepressure in the bellows 67 lags the change in pressure in the bellows66.

The bellows 66 and 67 are coupled to a rod 69 which pivots in seesawfashion about a fixed point 70. The rest position of the rod is set by aset point adjuster 71 that is coupled to one of the ends of the rod 69.A nozzle regulating vane 72 is coupled to the other end of the rod 59,and a portion of the vane in turn is coupled to a camtype proportionalband sector 73 by a' linkage 74 Air pressure is applied from a source ofreference pressure (not shown) via an input line 75 to thediiferentiator 14. Within the dilferentiator the input air pressurepasses through a filter 76 to a pair of inputs 77 and 78 of a diaphragmbooster unit 79. A small restriction 80 is located in the input line 77and restricts the flow of air into bellows section 81.

The diaphragm booster unit 79 comprises a lower bellows section 81 thatis connected to the input line 77. A pair of linkages 82 and 83mechanically couple the bellows section 81 to aflexible diaphragm 84attached to the sides of an outer tube 85. The diaphragm 84 is, in turn,coupled by a linkage 86 to an inner tube 87 located within the outertube 85. The inner tube 87 passes through and is pivotally coupled to asecond flexible diaphragm 88 attached to the sides of the outer tube 85.The inner tube 87 has air pressure admitted thereto via the input line78. A valve assembly 89 controls the flow of air from the inner tube,and air flows into an output line 90 only when the inner tube ispivotedabout a pivot point 91 in the diaphragm 88 to open the valve.

Air flow from the diaphragm booster unit 79 proceeds upon the line 90 toan output line 92 of the differentiating unit 14 and to an upper bellows93. The upper bellows is coupled to one end of a nozzle control arm 94that pivots about a pivot point 95. A lower bellows 96 is coupled to thenozzle control arm on the other side of the pivot point 95, and thebellows is freely exhausted to the outside atmosphere by virtue of twoexhaust lines 97 and 98. Attached to one end of the nozzle control arm94- is a tube 99 containing a nozzle 100 at the tip thereof. The tube 99is coupled to the diaphragm booster unit 79 and receives air pressureapplied thereto from the input line 77.

The operation of the difierentiator 14 is as follows. Assume that thedepth error signal applied on the line 65 is increasing. The increasingpressure is communicated to the bellows 66 before it is communicated tothe bellows 67. Thus, the rod 69 pivots about the point 70 as shown bythe arrow, thereby forcing the nozzle regulating vane 72 toward thenozzle 100. This increases the pressure within the nozzle tube 99, whichis communicated back to the diaphragm booster unit 79, and results in adownward motion of bellows section 81 which results in correspondingmotion of linkages 02, 83 and 86 through pivotal diaphragm 34.Consequently, motion of inner tube 87 results in the opening of valve89. Accordingly, an increase in air pressure occurs in the line which isdirectly coupled to the output line 92 of the ditferentiator.

Since the increased output pressure in the line 90 is also applied tothe upper bellows 93, the nozzle control rod 94 pivots about the point95, as shown by the arrows, thereby forcing the nozzle away from the endof the nozzle regulating vane 72. This results in a decrease in pressurewithin the nozzle tube 99, giving a feed back action similar to thatencountered in the booster section,

50 of the error computer 12 and a consequent rapid response of theoutput signal. Thus, because of the lagging action of the bellows 67,the output pressure from the difierentiator 14 is equal to the rate ofchange, with respect to time, of the depth error signal.

As maybe noted, when the depth error signal is constant and is notchanging, the pressures applied to the bellows 66 and 67 are equal, andthe nozzle regulating vane 72 assumes a rest position with respect tothe nozzle 100. In the rest position, the output pressure from thedifferentiator 14 is constant at a fixed value which corresponds to norate of change of the depth error signal.

Difierentiator 18 The output pressure from the diiferentiator 14, whichis indicative of the rate of change of the depth error signal, isapplied via an output line 101 to the differentiator 18, to the adder19, and to the instrumentation block 15. The differentiator 18 has thesame internal components as are included in the difierentiator 14, andfor this reason similar numerical designations for like components havebeen used in FIGURE 2A.

The output signal from the differentiator 18 thus is equal to the firsttime derivative of the output signal from the difierentiator 14, i.e.,the second time derivative of the depth error signal. This output signalis applied via output lines 102 and 1133 to the adder 19 and to theinstrurnentation block 15, respectively.

Instrumentation block As may be noted, the signals applied to theinstrumentation block 15 are the depth error signal (line '65) and itsfirst and second time derivatives (lines 101 and 103, respectively).Within the block, the depth error signal is applied to a depth errortransducer 104 which serves to transform the pneumatic depth errorsignal into an electrical signal, e.g., if such a transformation isdesired for convenience. The electrical depth error signal appears upona pair of secondary leads 105 of a transformer 106 Whose core 107 ispositioned in accordance with the pressure applied to the transducer.These secondary windings in turn may be coupled to any standardelectrical meter (not shown) to give an indication of the depth errorsignal.

Within the instrumentation block 15 the first and second derivativesignals are applied to a pair of associated adjustable pulsationdampeners 108 and 109, respectively, whose outputs on lines 110 and 111may be coupled to pneumatic test instruments (not shown). i

The instrumentation block 15 is provided for monitoring the essentialsignals that form the ultimate control signal used to position thesubmarine. Thus, the test instruments located therein may be mountedeither on a single panel, at some convenient central location, or atvarious separate locations within the submarine.

Adder The adder 19 has virtually the same internal components as doesthe diiferentiator 14 described above, and for this reason similarnumerical designations for like components have been used. Changes inthe connections of the components of the adder, however, are as follows.Bellows 67b is completely vented, input line 98b is completely closedoif, and input line 97b within the adder is coupled directly to the line102 from the differentiator 18. With these modifications, the adder sumstogether the input signals applied thereto from the differentiators 14and 13. This is apparent since the signal from the difierentiator 14 iscoupled only to the bellows 66b, providing the sole force on the nozzleregulating vane 72b, while the signal from the dififerentiator 18 iscoupled directly and only to bellows 96b, which moves the nozzle tube99b. Venting the bellows 67b eliminates the differentiating feature ofthe unit.

Composite signal generator The sum of the first and second derivativesof the depth error signal is applied via an output line 11 2 from theadder 19 to input line 980 within the composite signal generator 17.Like the other units of the control system, the internal components ofthe composite signal generator are similar to those included in thedifferentiator 14, and for this reason similar numerical designationsfor like components have been used. The following changes, however, havebeen made. Input line 97c is completely closed ofi, bellows 67c isvented, and the depth error signal, applied to the composite signalgenerator on line 65, passes to bellows 66c and to another bellows 113a.A pair of linkages 114c and 115a couple the diaphragm 1130 to asecondary cam 1160 whose movement actuates an arm 117s that swings theprimary cam 73c about its pivot point. Movement of the primary cam 73cswings the end of the nozzle regulating vane 72c toward or away from thenozzle 100c.

With the changes described, the output signal from the composite signalgenerator appearing on the line 92c within the generator is equal to thesum of the signal from the adder 19 and a modified depth error signal.This output signal is expressed by Equation 1 given above. That thecomposite signal generator generates such a signal is apparent from anexamination of the generator itself. That is, the input signal from theadder 19 is applied directly to the bellows %c which controls themovement of the nozzle control arm 940. This accounts for the first twofactors of Equation 1, namely, the first derivative and secondderivative depth error signals. Applying the depth error signal to thebellows 66c and 113s, both of which control the movement of the nozzleregulating vane 720, results in the addition of the third and finalfactor of Equation 1. Without the bellows 1130 the depth error signalwould be added directly to the signal from the adder 19; however, thebellows 113c modifies the depth error signal by a proportionality factorgiven as K in Equation 1.

Because it is the depth error signal that is applied to the bellows1130, the proportionality factor K is a variable which is a function ofthe depth error signal. The variation in K with the depth error may bechosen to be linear or non-linear, to give any desired type of response,i.e., one which is either positive or negative with respect to the deptherror. In the present application of this invention to submarinehovering, it is desirable that K increases as the magnitude of the deptherror itself increases.

The output signal from the composite signal generator, which is aweighted signal taking into account the depth error signal and its firstand second time derivatives, may be used in its pneumatic form toactuate suitable control equipment for changing the depth of thesubmarine. However, at times it may be desirable to elfect a translationof the control signal from its pneumatic form into another form, such asan electrical control signal. Apparatus to effect such a translation isshown in FIG- URE 2B as the output translator 21, and a description ofthis follows.

Output translator The output signal from the composite signal generator17 is applied on a line 118 to the output translator 21. Within thetranslator the pneumatic input signal is applied to a bellows 119 whichactuates a movable bar 129. The bar 12a is urged downward by a spring121 coupled between the bar 126 and another bar 122. The movement of thebar 122 is determined by the movement of a cam 12-3 that is mechanicallycoupled to a vertical gear rod 124. The gear rod 124 is in turn coupledat the top thereof to a diaphragm 125 that is urged downward against.the restraining force of a spring 126 by a source of air pressuresupplied to the diaphragm from an input line 127. The input line 127 iscoupled to a filter 128 which receives air pressure through a valve 129that is actuated by the movable bar 120. The valve 129 receives airpressure from a source of reference pressure (not shown) that is appliedvia an input line 130 through a filter 131.

To understand the operation of the output translator, assume that thesignal from the composite signal generator 17 is increasing. In thisevent, the movement of the movable bar 123 is upward as shown in thefigure, resulting in the delivery of a greater supply of air to thediaphragm 125 and a consequent downward movement of the vertical gearrod 124. Downward movement of the gear rod results in counterclockwisemovement of a gear 132 and clockwise movement of a gear 133. Theclockwise movement of the gear 133 in turn moves an arm 134 on arhe'ostat 135, thus changing the values of the resistances seen lookinginto output terminals 136 connected to the rheostat. The terminals resmay be coupled to any well-known electrical gain device (not shown)whose gain depends upon the magnitudes of associated resistances, and inthis fashion the output translator eflects a translation of a pneumaticcontrol signal into an electrical control signal. Such a gain device,e.g., would normally be incorporated in the servomechanism 22 of FIGURE1.

Although the submarine hovering system described in detail above its apneumatic-electric control system, the invention is not in any waylimited thereto. Such a control system could be entirely pneumatic,hydraulic, or electrical, for example, or portions of the system mightinvolve any one or more of these parameters. This is illustrative of oneof the ways in which the invention might be modified withoutconstituting a departure from the spirit of the invention. Suchmodifications and changes as these, and other immaterial changes, shouldall be deemed to lie well within the scope of the following claims whichare set forth as follows to define this invention.

I claim:

1. The method of positioning a submarine at a predetermined depthcomprising the steps of generating an error signal representative of thedifierence between the depth assumed by the submarine and thepredetermined depth, differentiating the error signal to generate afirst derivative signal, differentiating the first derivative signal togenerate a second derivative signal, multiplying the error signal by afactor substantially equal to the error signal raised to a power equalto at least one, and combining the multiplied error signal, the firstderivative signal and the second derivative signal to generate acomposite control signal, whereby the composite control signal may beutilized to reposition the submarine.

2. In a'control system in which a signal is generated for positioning avehicle at a predetermined level in a fluid, means for multiplying thesignal by a factor substantially equal to the difference between thelevel assumed by the vehicle in the fluid and the predetermined level,thereby to generate a Weighted signal.

3. In apparatus for positioning a vehicle at a predetermined levelWithin a fluid, means for generating a single control signal usable toactuate apparatus for repositioning the vehicle within said fluid,comprising means for generating an error signal substantially equal tothe difference in pressure exerted by said fluid at said predeterminedlevel and the level then assumed by said vehicle, means for generating avelocity signal and an 9 acceleration signal from said error signal,means for multiplying the magnitude of said error signal by a factorproportional to its unadjusted magnitude with respect to a referencemagnitude which is equal to at least one, and means for combining saidvelocity, said acceleration and said multiplied error signals thereby togenerate a single control signal.

4. In a control system in which an error signal and at least one timedifferentiated error signal are utilized to position a vehicle within afluid, means for generating a composite control signal comprising meansfor multiplying said error signal by a factor proportional to itsmagnitude which is equal to at least one, and means for adding togethersaid multiplied error signal and said time differentiated error signalto produce a composite control signal.

5. Apparatus to position a submarine at a predetermined depth comprisingmeans for generating an error signal representative of the differencebetween the water pressure at the depth actually assumed by thesubmarine and a reference pressure representative of the water pressureat said predetermined depth, means for differentiating said error signalwith respect to time to generate a first derivative signal, means fordifferentiating said first derivative signal with respect to time togenerate a second derivative signal, means for adding said first andsaid second derivative signals to generate a first sum signal, means formultiplying the magnitude of said error signal by a factor substantiallyequal to the error signal raised to a power equal to at least one, meansfor adding said first sum signal and said multiplied error signal togenerate a correction signal, and means responsive to said correctionsignal to reposition the submarine.

References Cited by the Examiner UNITED STATES PATENTS 1,988,458 1/35Minorsky. 2,259,600 10/41 Alkan.

2,938,435 5/60 Gille 8941 3,086,394 4/63 Peck 235--l83 FOREIGN PATENTS536,537 5/41 Great Britain. 609,705 10/48 Great Britain.

BENJAMIN A. BORCHELT, Primary Examiner.

SAMUEL FEINBERG, CHESTER L. JUSTUS,

Examiners.

1. THE METHOD OF POSITIONING A SUBMARINE AT A PREDETERMINED DEPTHCOMPRISING THE STEPS OF GENERATING AN ERROR SIGNAL REPRESENTATIVE OF THEDIFFERENCE BETWEEN THE DEPTH ASSUMED BY THE SUBMARINE AND THEPREDETERMINED DEPTH, DIFFERENTIATING THE ERROR SIGNAL TO GENERATE AFIRST DERIVATIVE SIGNAL, DIFFERENTIATING THE FIRST DERIVATIVE SIGNAL TOGENERATE A SECOND DERIVATIVE SIGNAL, MULTIPLYING THE ERROR SIGNAL BY AFACTOR SUBSTANTIALLY EQUAL TO THE ERROR SIGNAL RAISED TO A POWER EQUALTO AT LEAST ONE, AND COMBINING THE MULTIPLED ERROR SIGNAL, THE FIRSTDERIVATIVE SIGNAL AND THE SECOND DERIVATIVE SIGNAL TO GENERATE ACOMPOSITE CONTROL SIGNAL, WHEREBY THE COMPOSITE CONTROL SIGNAL MAY BEUTILIZED TO REPOSITION THE SUBMARINE.